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Block #1,611,502

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2016, 9:35:33 PM Β· Difficulty 10.6061 Β· 5,230,288 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
e1a8dc1bc99be42a987ae07bc57dae3349a91ec2f058a41b10a53cac88f2f695
View on Chainz β†—

Height

#1,611,502

Difficulty

10.606059

Transactions

1

Size

198 B

Version

2

Bits

0a9b26a8

Nonce

233,915,670

Timestamp

6/2/2016, 9:35:33 PM

Confirmations

5,230,288

Mined by

⛏️ P2SHASD15KFSaaQ66YtdeSfGN5r29Ra2Kb7n7R

Merkle Root

b624bf9680c2e80bffb5a6850db7a8c4a68cb3cfd3b961ad16cc43b05ee657a9
Transactions (1)
Coinbaseb624bf9680c2e8…cc43b05ee657a9
1 in β†’ 1 out8.8800 XPM109 B
ASD15KFS…a2Kb7n7R
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.560 Γ— 10⁹³(94-digit number)
25604720926420033434…65824652350345480801
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.560 Γ— 10⁹³(94-digit number)
25604720926420033434…65824652350345480801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.120 Γ— 10⁹³(94-digit number)
51209441852840066869…31649304700690961601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.024 Γ— 10⁹⁴(95-digit number)
10241888370568013373…63298609401381923201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.048 Γ— 10⁹⁴(95-digit number)
20483776741136026747…26597218802763846401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.096 Γ— 10⁹⁴(95-digit number)
40967553482272053495…53194437605527692801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.193 Γ— 10⁹⁴(95-digit number)
81935106964544106990…06388875211055385601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.638 Γ— 10⁹⁡(96-digit number)
16387021392908821398…12777750422110771201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.277 Γ— 10⁹⁡(96-digit number)
32774042785817642796…25555500844221542401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.554 Γ— 10⁹⁡(96-digit number)
65548085571635285592…51111001688443084801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.310 Γ— 10⁹⁢(97-digit number)
13109617114327057118…02222003376886169601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,978,698 XPMΒ·at block #6,841,789 Β· updates every 60s
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